Question: Find the greatest common factor of $44$ and $66$.
Answer: The greatest common factor (GCF) is the largest number that is a factor of both $44$ and $66$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}44 &=2\cdot2\cdot11\\\\\\\\ 66&=2\cdot3\cdot11 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}44 &=2\cdot2\cdot{11}\\\\\\\\ 66&=2\cdot3\cdot{11} \end{aligned}$ Each number shares the factors ${2}$ and ${11}$, so the GCF is $2\cdot{11}={22}$. The greatest common factor of $44$ and $66$ is $22$.